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Figure 9 | The Journal of Mathematical Neuroscience

Figure 9

From: A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy

Figure 9

Networks of four nodes: escape times. (a): Comparison of Equation 5 with numerical escape time data for four-node networks. Each point represents one topologically distinct network. The vertical axis represents the escape time, E [ τ ] , for this network with large β (from simulations using β = 100). The horizontal axis represents the expression N- | u | N e (see Equation 5). Since the vertical scale is logarithmic the apparent straight line relationship suggests an exponential relationship as predicted in Equation 5. The dotted line is a fit, with equation y = exp(ax + b). Like the right-hand side of Fig. 8, there are groupings of networks having near identical escape times. Graphs from a few groups are plotted as coloured dots. Since these data-points are very close together, they are hard to distinguish visually. Instead each group is circled and the number of graphs within the group is indicated. The remaining 71 graphs are shown as black dots. (b): Example graphs to illustrate the groups identified in (a). Groups of graphs are distinguished by their FTC and whether or not they are balanced or unbalanced. A balanced graph is a graph in which each node has the same number inputs as outputs (in which case |u| = 0). 1: This is a group of 60 graphs each of which has a single node as its FTC, like those in Fig. 7b. 2: 17 graphs each having a 2-node strongly connected network as its FTC, (Fig. 7c. 3u1: 7 graphs each having a particular 3-node graph (9 from Fig. 7) as its FTC. 3u2: 7 graphs each having a particular 3-node graph (10 from Fig. 7) as its FTC. 3b: 11 graphs each of which has a balanced 3-node graph as its FTC (in a balanced graph, each node has the same number of inputs as outputs, i.e., |u| = 0). 4b: 12 strongly connected graphs each of which is balanced.

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